Nikolaus Conference 2018

Speaker: Emily Norton (Bonn)

Title:Do Finite Groups of Lie Type and Cherednik Algebras Speak to Each Other?

Abstract:

This talk is about unexplained coincidences of decomposition numbers
between seemingly unrelated objects. The decomposition matrix of a
unipotent block of a finite group of Lie type in cross characteristic
has a square submatrix indexed by the unipotent characters. Many
low-rank examples of these decomposition matrices were computed in
recent years by Dudas and Malle. In many cases, the matrices obtained
are identical on the principal series characters, which are indexed by
the irreducible characters of the Weyl group, to decomposition matrices
I computed for the rational Cherednik algebra at a corresponding
parameter. I will explain structural parallels and differences between
the two theories and summarize the numerical data, and I will provide
examples that show that we cannot in general expect the decomposition
matrix of the Cherednik algebra to appear as a submatrix of the
decomposition matrix of the finite group.